Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 21I / b

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- Solution b

Solution

Complex Stone-Weierstrass requires a self-conjugate unital subalgebra separating points; apply real Stone-Weierstrass to real and imaginary parts. Finite sums

f (x) g (y)

form such a self-conjugate unital subalgebra of

C (K \times L)

and separate points, so they are dense.

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